Question

In Young’s double slit experiment, to change the bandwidth from $\beta$ to $\frac{\beta}{4}$ without changing the experimental setup, the wavelength of light $\lambda$ used must be changed to

• A. $4\lambda$
• B. $16\lambda$
• C. $\frac{\lambda}{4}$
• D. $\frac{\lambda}{16}$
• E. $8\lambda$

Hint:

In Young’s double slit experiment, fringe width is directly proportional to the wavelength of the light used.

Answer 1

The Correct Option is C

Step 1: The fringe width (bandwidth) $\beta$ in Young’s double slit experiment is given by: \[ \beta = \frac{\lambda D}{d} \] where $\lambda$ is the wavelength of light, $D$ is the distance between the screen and the slits, and $d$ is the separation between the slits. 
Step 2: Since $D$ and $d$ remain unchanged, the bandwidth is directly proportional to the wavelength: \[ \beta \propto \lambda \] 
Step 3: To reduce the fringe width from $\beta$ to $\frac{\beta}{4}$, we must reduce the wavelength accordingly: \[ \lambda' = \frac{\lambda}{4} \] Step 4: Therefore, the correct answer is (C).